Quale informatica? Tecnica e metodologia http://tfa.di.uniroma1.it Anna Labella L’informatica una scienza sperimentale? I calcolatori sono strumenti fisici I calcolatori sono la materializzazione del nostro pensiero L’informatica potrebbe esistere con calcolatori completamente diversi ……. Cos’è l’informatica? Cos’è utile insegnare nella scuola? •Computer literacy •Programming skills •Applications like games, robots and simulations Cos’è utile insegnare nel TFA? Ai futuri docenti non dobbiamo insegnare le basi né temi avanzati di informatica: le prime sono conosciute, i secondi non servono Dobbiamo convincere i futuri insegnanti che l’informatica, come la matematica, è un metodo L’informatica: una disciplina particolare Computational thinking Problem solving Interdisciplinarietà Il metodo informatico L’informatica come disciplina, ma soprattutto come metodo nell’insegnamento. Pensare come un informatico, anche prescindendo eventualmente dalla tecnologia. sperimentazioni fatte nel mondo in questo senso. Astrazione ed automazione. Il pensare informatico a confronto con il pensare matematico ed altri tipi di “pensiero” nell’educazione dei giovani del 21° secolo. Il pensare informatico e l’interdisciplinarietà. Cos’è il Computational Thinking? Cos’è il Computational Thinking? Many adjectives describe modes of thinking: Abstract, analytic, conceptual, concrete, constructive, creative, critical, deductive, strategic, synthetic, tactical and… computational and procedural. J. Wing My Grand Vision for the Field Computational thinking will be a fundamental skill used by everyone in the world by the middle of the 21st Century. Just like reading, writing, and arithmetic. Imagine every child knowing how to think like a computer scientist! Incestuous: Computing and computers will enable the spread of computational thinking. In research: scientists, engineers, …, historians, artists In education: K-12 students and teachers, undergrads, … J.M. Wing, “Computational Thinking,” CACM Viewpoint, March 2006, pp. 33-35. http://www.cs.cmu.edu/~wing/ Le due A del CT La prima A del CT Abstractions are our “mental” tools The abstraction process includes Choosing the right abstractions Operating simultaneously at multiple layers of abstraction Defining the relationships the between layers La seconda A del CT The power of our “mental” tools is amplified by our “metal” tools. Automation is mechanizing our abstractions, abstraction layers, and their relationships Mechanization is possible due to precise and exacting notations and models There is some “computer” below (human or machine, virtual or physical) Le due A combinate Computing is the automation of our abstractions They give us the audacity and ability to scale. Computational thinking choosing the right abstractions, etc. choosing the right “computer” for the task Il Problem solving David Moursung : Introduction to problem solving in the information age http//uoregon.edu/˜moursund/dave/index.html Cos’è il problem solving? Critical thinking Quale matematica nel secolo? La relazione tra matematica e informatica Prof. Madhu Sudan - Massachusetts Institute of Technology (MIT) ° 21 Cos’è la matematica? Temi Metafore Linguaggio Rigore Temi Geometria Aritmetica Algebra Combinatoria Calcolo Infinitesimale Probabilità …. Perché non ? Musica Astronomia Calcolo Logica ……. Una scorsa storica Schema Problem Formalization Machine Algorithm Tavola Partition Division Canon One or more congruences ? Riddle One or more linear equations ? Abacus Algorithm Mensa for the pitagorica abacus ? Tabula mirifica ? ? Matematica Divisione su abaco divisore dividendo resto quotiente 6 4 5 4 9 5 2 1 4 4 2 6 2 1 1 9 5 2 1 9 4 2 5 9 3 6 2 1 1 1 1 549 : 6 1 2 3 4 5 6 7 8 9 2 4 6 8 10 12 14 16 18 3 6 9 12 15 18 21 24 27 4 8 12 16 20 24 28 32 36 5 10 15 20 25 30 35 40 45 6 12 18 24 30 36 42 48 54 7 14 21 28 35 42 49 56 63 8 16 24 32 40 48 56 64 72 9 18 27 36 45 54 63 72 81 Rythmomachia (XI sec.) ?????? 1 2 3 4 5 6 7 8 9 2 4 6 8 10 12 14 16 18 3 6 9 12 15 18 21 24 27 4 8 12 16 20 24 28 32 36 5 10 15 20 25 30 35 40 45 6 12 18 24 30 36 42 48 54 7 14 21 28 35 42 49 56 63 8 16 24 32 40 48 56 64 72 9 18 27 36 45 54 63 72 81 Musica Labella,A. and Scozzafava, C.: Music and algorithms: a historical perspective. Studi Musicali Volume: 32 Issue: 1 (2003-01-01) p.3-25. ISSN: 0391-7789 Canone infinito 1* 2 3* 4 2 1* 2 3* 4 1* 2 h(n+k) ≈ h(n) Two voices at unisono 3* 2 4 Two voices at a h(n+k) ≈ h(n) + h given interval 1 2 3 1 5* 4 7 3 4 1 2 5 3 1 3 4 5 5 5* 6* 7 3* 4 1* 2 5* 3* 4 1* 2 3* 3* 2 6* 5* 4 5* 6* 3* 4 1* 2 3* 2 6* 5* 4 8* 7 5 2 8* 9 5* 6* 7 8* 3* 4 3* 2 6* 5* 4 8* 7 9 1* 3* 2 6* 5* 4 h(n+k1) ≈ h(n) + h1 h(n+k2) ≈ h(n) + h2 …….. More voices 3* 2 5* 6* 7 1* 2 3* 2 1* Canone cancrizzante e inverso h(n) ≈ h(N - n) ….. Cancrizzante 1 1 2 7 3 1 Inverse recursion? 4 5 7 6 1 7 1 6 7 5 4 3 2 1 h(n) ≈ [h(n-1)-h’(n-1)]+ 2[h(n)-h(n-1)] ….. Canone Mensurale h(n) ≈ h(q n -i) 5 2 0≤ i ≤ q-1 3 3 3 2 7 5 5 1 5 8 3 8 6 6 4 7 5 6 5 1 6 6 1 8 8 10 7 10 9 6 5 6 8 4 Indovinelli Alcuino di York Problema 26: Ilcane e la volpe Un cane insegue una volpe che è 150 piedi più avanti di lui. La lepre fasalti di di 7 piedi, il cane di 9. Dopo quanti salti il cane raggiunge la lepre? In 75 salti, cioè 150:2 The computational attitude: algorithms An algorithm is a step-by-step set of directions guaranteed to achieve a task, which may be to solve a particular problem, in a finite number of steps. http://iae-pedia.org/Computational_Thinking#Computational_and_Procedural_Thinking A heuristic is like an algorithm except that accomplishment of a specific task or solution of a specific problem is not guaranteed. Algorithms and computers A computer is a machine that can automatically, rapidly, and accurately carries out the steps in certain types of procedures. Computer programmers think in terms of solving problems and accomplishing tasks through the use of procedures. Attenzione al linguaggio Language and philosophy Sophists and philosophers Language and mathematics Mathematical rigor The discovery of “languages” Wittgenstein: linguistical games The “analogy” Transfer cocepts and methods from one language to another one: useful, but very dangerous!!! Scientifical languages (and others) •"Measuring" the diagonal of the square • Establish the following "equations": Fe +H2SO4 = FeSO4 +H2 Cu +H2SO4 = CuSO4 +H2 Denotational antinomy • 343 is 73 • 343 is three-digit • 73 is three-digit A logic for every language (also in computer science) Axioms and rules la comunicazione diretta DIRETTA LINGUAGGIO CORPOREO ODORARE SEGNI SUONARE PARLARE la comunicazione mediata In modo tradizionale TESTO DISEGNO RIPRODUZIONE ANALOGICA IMMAGINI SCRITTURA SUONI la comunicazione mediata via computer TESTO SUONI IMMAGINI ANALISI SINTESI INTERPRETAZIONE. PR & IP SCENE ANALYSIS Visual Programming Spreadsheet DOCUMENT IMAGE OCR Visual Query Systems Visual Languages Scientific Visualization Algo Animation SW Visualization Code Animation Process Visualization Environment Dev. Data Animation la comunicazione mediata via computer TESTO SUONI IMMAGINI ANALISI SINTESI INTERPRETAZIONE. PR & IP SCENE ANALYSIS Visual Programming Spreadsheet DOCUMENT IMAGE OCR Visual Query Systems Visual Languages Scientific Visualization Algo Animation SW Visualization Code Animation Process Visualization Environment Dev. Data Animation Old and new metaphores Space Time Game Images Light Grammars Biological structures ……. Interfaces construction Interface is a program allowing a user to use programs contained in a computer Hence it is aimed to “non technical people” (Myers 93) Difficulty in understanding users attitudes Complexity Balance among graphic, writing, languages, detail levels, social- legal constraints, implementation time t... Theories and guidelines are not sufficient Visual metaphors Use of visual metaphors in a didactical context An example: e-learning for deaf people The problem Difficulty in learning to read and to write Diacronical and syncronical arrangement of language Sign language and representation difficulty New tecnologies and iconical information Introduction of a video in LIS? This is possible, but it does not solve the problem 58 Metafora e embodiement La matematica è un campo di “criticità sensoriale” anche per persone senza deficit, perché “astratta” e “non raccontabile” Necessità di metafore spaziali e non: geometria, teoria degli insiemi, operatività… Informatica e interdisciplinarietà Applicazioni Ambienti virtuali Videogiochi E-learning